Problem: Solve for $x$ and $y$ using elimination. ${-3x-3y = -30}$ ${-2x+3y = 20}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-5x = -10$ $\dfrac{-5x}{{-5}} = \dfrac{-10}{{-5}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-3x-3y = -30}\thinspace$ to find $y$ ${-3}{(2)}{ - 3y = -30}$ $-6-3y = -30$ $-6{+6} - 3y = -30{+6}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 2}$ into $\thinspace {-2x+3y = 20}\thinspace$ and get the same answer for $y$ : ${-2}{(2)}{ + 3y = 20}$ ${y = 8}$